Wind resources at Horns Rev

REPORT 

Wind Resources at Horns Rev 

Eltra PSO-2000 Proj. nr. EG-05 3248 

Måleprogram for vind, bølger og strøm for Horns Rev / 

Programme for measuring wind, wave and current at Horns Rev 

Summary 

December 2002 

Phone: +45 79 23 33 33 

Fax: +45 75 56 44 77 

Our ref.: Anders Sommer 

Report no.: D-160949 

Project no.: 11746.01.06 

Page 1 of 69 

Since May 1999, meteorological measurements have been conducted at Horns Rev with 

an overall coverage of more than 99%. 

The measurement system was designed to operate meteorological instruments together 

with a sonic anemometer, a wave height sensor and an instrument to measure current 

speed and direction. 

The Horns Rev meteorological observations from the offshore measurement site have 

been analysed and compared with long-term wind speed time series to produce 

estimates of the wind resources. Different methods have been used in this process, and 

the values presented here are the best estimates based on all results, taking into account 

the strengths and weaknesses of each method. 

In addition to the wind resource predictions, the data sets have been used in new 

analyses focussing on meteorology, turbulence, extreme winds and wind and wave 

interactions. The relationship between wind speed, turbulence and fetch are highly 

complex; at lower wind speeds, stability effects are important, while the wind and wave 

interaction seem to dominate at higher wind speeds. 

This report was written in co-operation with Kurt S. Hansen, Department of Mechanical 

Engineering, Fluid Mechanics Group, Technical University of Denmark. 

Verified: Approved: 

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permission, and the contents thereof must not be imparted to engineering company specialised Kraftværksvej 53 

a third party nor be used for unauthorised purposes in energy and environment DK-7000 Fredericia

energy. environment. knowledge. Page 2 of 69 

Table of Contents 

1. SITE AND DATA ASSESSMENT......................................................................... 4 

1.1 SITE DESCRIPTION.............................................................................................. 4 

1.2 DESCRIPTION OF MEASUREMENTS SYSTEM ........................................................ 4 

1.2.1 Primary meteorological system ................................................................ 4 

1.2.2 Met back-up system................................................................................... 8 

1.2.3 Sonic system............................................................................................ 11 

1.3 QUALITY CONTROL.......................................................................................... 13 

1.3.1 Determination of spikes.......................................................................... 13 

1.3.2 Determination of signal drop-outs.......................................................... 14 

1.3.3 Determination of signal stationarity....................................................... 14 

1.4 DATA OVERVIEW ............................................................................................. 15 

1.4.1 Directional sensitivity analysis............................................................... 15 

1.4.2 Primary met system................................................................................. 18 

1.4.3 Back-up met system................................................................................. 19 

1.4.4 Sonic system............................................................................................ 20 

2. STATISTICS .......................................................................................................... 20 

2.1 WIND SPEED AND TURBULENCE....................................................................... 20 

2.2 WIND DIRECTION ............................................................................................. 25 

2.3 AMBIENT TEMPERATURES................................................................................ 26 

2.4 WIND PROFILES................................................................................................ 29 

3. 3-D MEASUREMENTS ........................................................................................ 30 

3.1 SONIC MEASUREMENT SYSTEM - BASIC STATISTICS ......................................... 30 

4. UPDATING RESOURCE ESTIMATES ............................................................ 34 

4.1 CHARACTERISING THE LONG-TERM CLIMATE AT HORNS REV.......................... 34 

4.2 RESOURCE ESTIMATES USING DIFFERENT METHODOLOGIES ............................. 35 

4.2.1 Weibull method ....................................................................................... 35 

4.2.2 Measure-correlate-predict (MCP).......................................................... 37 

4.3 COMPARISON WITH PREVIOUS ESTIMATES ....................................................... 41 

5. STABILITY AND CLIMATE.............................................................................. 42 

5.1 SHEAR EXPONENT DISTRIBUTION ..................................................................... 42 

5.2 DISTRIBUTION OF GUSTS.................................................................................. 43 

6. WIND-WAVE-ROUGHNESS.............................................................................. 45 

6.1 MARINE DATA OVERVIEW ................................................................................ 47 

6.2 MARINE STATISTICS......................................................................................... 48 

6.2.1 Time series plots..................................................................................... 48 

6.2.2 Waves...................................................................................................... 50 

6.2.3 Currents.................................................................................................. 59 

6.3 NUMERICAL SIMULATIONS MODELS ................................................................. 61 

6.4 RELATIONSHIP BETWEEN WAVE HEIGHT AND TURBULENCE INTENSITY............ 62 


Tech-wise A/S is an international consulting Tech-wise A/S 

engineering company specialised Kraftværksvej 53 

in energy and environment DK-7000 Fredericia


7. EXTREME EVENTS ............................................................................................ 64 

8. UNCERTAINTIES ................................................................................................ 67 

9. CONCLUSION ...................................................................................................... 68 

10. REFERENCES ...................................................................................................... 69 






1. Site and data assessment 

1.1 Site description 

The meteorological mast at Horns Rev is located approximately 20 km west of 

Blåvands Huk. Its position is 7°47,217'E 55°31,208'N (WGS84) and its UTM 

coordinates are 423.412E 6.153.342N (WGS84 Zone 32). The location of the mast is 

shown in Figure 1.1. The distances to the nearest shore (fetch distances) are given in 

Figure 1.3. 

Figure 1.1 Location of met mast at Horns Rev, west of Jutland 

1.2 Description of measurements system 

A square lattice mast was erected on a monopile close to the projected wind farm site at 

Horns Rev. In mid-May 1999 the meteorological measurement programme was initiated 

and later, in June 1999, the marine measurement programme started. 

The measuring system comprises a total of five independent systems: 

1. Primary meteorological system (10 min). 

2. Back-up meteorological system (10 min). 

3. Sonic meteorological system (20 Hz). 

4. Wave height measuring system. 

5. Current and water level measuring system. 

1.2.1 Primary meteorological system 

In 1999 the mast at Horns Rev was instrumented with the system shown in Figure 1.2. 

The data acquisition (DAQ) system is capable of collecting and storing statistical values 






from the meteorological instruments. The meteorological measurements introduced in 

May 1999 include four-level wind speeds as well as wind directions, temperatures, 

atmospheric pressure, solar radiation and lightning detection. The four measurement 

levels are 62, 45, 30 and 15 m above DNN (Danish Normal Zero). 

Wind speed measurements are performed with Risoe Cup Anemometers. They have 

been used worldwide during the last 20 years by meteorological institutes, scientific 

laboratories, research laboratories, and industry. For the wind direction measurements 

ED wind direction sensors are used. This type of wind direction sensor is used 

worldwide at wind farms, airports, and meteorological stations. These sensors are 

highly suited for saline environments featuring high wind speeds and wide temperature 

ranges. 

Statistical values from the primary met system are sent to an onshore database once an 

hour, and shown on a local web page: http;//212.130.241.250/hornsrev. 






Figure 1.2 Instrumentation primary meteorological system 






To keep the power consumption at an absolute minimum, two standard data loggers 

were selected to scan the sensors. The sampling rate is 1Hz, and before being stored in a 

flash RAM unit the data are condensed to 10-min mean values together with maximum, 

minimum, and standard deviations for the averaging period. For the wind speed sensors 

a 5-s gust is calculated as a mean of five consecutive 1 Hz values. The storage capacity 

of the flash RAM unit is equivalent to 9 months of data. 

The main components of the power supply were designed as simply as possible, 

comprising a matrix of 2 x 5 x 50 W photovoltaic cells charging 25 NI-Cd batteries with 

a capacity of 1070 Ah. The power system is capable of delivering 16 W continuously. 

However, due to a miscalculation on the part of the erection contractor, the mast is 

oriented + 33.1 ° wrong. Because of this mistake the photovoltaic cells deviate 33.1 ° 

from facing directly south, and are therefore unable to achieve the envisaged power 

production. To compensate for that another 4 x 50 W photovoltaic cells were put up to 

deliver the needed power capacity. 

Figure 1.3 Fetch distances at Horns Rev 

Direction Fetch (km) 

N 280 

NNE 62 

NE 36 

ENE 21 

E 25 

ESE 44 

SE 62 

SSE 80 

S 190 

SSW 240 

SW 700 

WSW 500 

W 600 

WNW 600 

NW 700 

NNW 700 

Every spring and autumn the primary met system is subjected to regular maintenance, 

and all sensors are replaced with newly calibrated sensors. Because the project has an 

extra set of sensors to replace the existing ones, the system is up and running again in 

only a few hours, and only one trip to the offshore mast is needed. 






Figure 1.4 Meteorological mast, platform and photovoltaic cells 

1.2.2 Met back-up system 

The met back-up system is instrumented with Aanderaa wind and direction sensors and 

with an Aanderaa recorder. Aanderaa recorders are low power systems designed to 






operate in harsh conditions with a proven track record of reliability. The back-up met 

system is a completely separate data logger system comprising wind speed, wind 

direction and atmospheric pressure. The sensors are placed in the top section of the mast 

at level 58 m ensuring maximum data coverage in failure situations. The sensors are 

also used for validation of the primary met system measurements. Data from the backup 

met system are stored in Data Storage Units (DSU) with a capacity of more than 6 

months of measurements. 

The back-up met system has a separately power supply, an internal battery that can 

supply the sensors and storage units for more than 6 months. The DSU and the battery 

are replaced at each maintenance visits. 






Figure 1.5 Instrumentation back-up met system 






1.2.3 Sonic system 

In October 1999, a 3D-sonic wind measurement system was installed at the 

meteorological mast at level 50 m above DNN. Time series from the fast response sonic 

anemometer are collected and stored on a laptop pc, which is capable of storing time 

series (20 Hz data) from more than 6 months. Two identical laptops were used for data 

storage; one was offshore collecting data on the meteorological mast, and one was 

brought onshore with data from the last measuring period. The two laptops were 

exchanged at the maintenance visits. 

By November 2001, a new software system for the data storage laptop had been 

developed. Now only one laptop is needed, and the data are brought onshore on flash 

cards at each maintenance visit. 

Statistical 10-min mean values from the sonic system are also automatically sent to an 

onshore database by SMS every hour, and can also be accessed on the Internet with a 

personal login and password. 






Figure 1.6 Instrumentation sonic system 

The sonic system has a separate power supply system, 4 x 50 W photovoltaic cells, and 

an 0.3 A wind turbine that charges 20 batteries with a capacity of 210 Ah. The power 

system is capable of delivering 24 W continuously. 






1.3 Quality control 

Visual inspection 

Once a month, the wind data are inspected visually, the data series are plotted with a 

data validating tool kit, and quality codes are directly written into the database. 

Data screening 

In addition to the visual inspection of the data, which is conducted when new data are 

collected, a screening procedure has been developed to identify data, which could be 

faulty. This procedure is used to verify the data quality of huge amounts of 

measurements. Typically these measurements are stored as statistic values (mean (μ), 

standard deviation (σ), maximum and minimum values), where each set of values 

represents a period of ten minutes: 

The data screening procedure is performed in 3 steps: 

1) Determination of spikes 

2) Determination of drop-outs 

3) Determination of periods with stationarity 

One reading is defined as one single value (mean, standard deviation, maximum, or 

minimum) representing one 10-min period. All readings are marked with a code = 0 

from the start and a spike, a drop-out, or stationarity indication, which gives a new code 

value according to the code numbers listed below. 

1.3.1 Determination of spikes 

Table 1.1 Definition of quality codes 

Code Item 

0 The reading is not validated 

1 The reading is validated 

2 The reading contains a spike 

3 The reading contains a drop-out 

4 - 

5 - 

9 The reading is faulty 

A spike is defined as an abnormal deviation from the recorded mean value. For this 

procedure four statistical values (mean, standard deviation, minimum and maximum) 

are used. 

A spike occurs if: 

(1) |maximum-μ| > 4 × σ or 

(2) |μ-minimum| > 4 × σ 






All spikes (>4×σ) are identified by means of a screening procedure and inspected 

afterwards, but only significant spikes are marked with a code = 2. The second 

condition (2) could result in code = 3, which indicates a signal drop to zero. 

This procedure is only applicable for wind speed signals, while it is based on both 

maximum and minimum values. 

1.3.2 Determination of signal drop-outs 

1) The wind speed signal drop-out is determined as a period with low (= zero signal) 

values corresponding to the minimum signal reading (< 0.1 m/s). 

2) Furthermore, periods with low signal activity (σ


1.4 Data overview 

The data coverage rate for the measurement systems is shown in the table below. 

Table 1.3 Data coverage rate for the meteorological measurement systems. 

Measuring system Data period Hours Data coverage 

Primary met. system 

Back-up met system 

Sonic System 

May 1999–Nov. 2002 

May 1999–Nov 2002 

October 1999–Nov. 2002 

1.4.1 Directional sensitivity analysis 

30638 

30359 

26888 

99.05% 

87.99% 

37.35% 

The directional sensitivity has been investigated for wind vanes mounted at three 

different heights (28, 43 and 60 m above DNN) and is based on more than 21,000 hours 

of measurements recorded in the wind speed range (5–25) m/s. 

The reference height is 60 m and the bin-averaged differences (bin size =2°) are shown 

on Figure 1.7-a. The maximum absolute difference is measured in the northern direction 

and decreases towards the south. All three vanes are free of wake effects in the VSV 

sector (258 ±90°), although they do not agree very well (+2/-3°) even in this sector. The 

best agreement has been obtained for 180° ±35°. 

This analysis recommends that the wind direction measured at height 60 m be used, and 

not to merge directional measurements from the other levels. The uncertainty of the 

absolute directional measurement is ±4°. Figure 1.7-b shows that the mast wake 

dominates the measurements in direction 20–45°, corresponding to a boom direction of 

212°. The average standard deviation of the wind direction measurement is approx. 4° - 

in free, undisturbed winds. 






Figure 1.7 Directional behaviour measured at Horns Rev, level 28, 43 and 60 m. 

Mast effects 

The mast speed-up and mast wake effect at three different levels (15, 30 and 45 m) have 

been investigated for wind speeds between 5 and 25 m/s with reference to the wind 

speed direction measured 60 m above sea DNN. Each level is represented with 

measurements recorded in the SV and NE directions and the cup anemometer locations 

at each level are listed in Table 1.4. 

The mast effect is determined as the ratio SV/NE, which is bin-averaged against the 

wind direction and shown in Figure 1.9-a. This figure shows a very distinct wake effect 

at all three levels, and it is recommended to use the free, undisturbed wind signal for 

further analysis. The recommended sectors with free, undisturbed wind speeds are listed 

in Table 1.5. 

It should be noted that the large deviations in Figure 1.9-a mainly reflects the deficits 

measured in the wake of the mast. The difference in the ratio from level to level, mainly 

reflects the difference in the mast solidity and boom length. 






Table 1.4 Mast and boom dimensions 

Level Dimensions Diagonal Boom length 

62 m - cup Top mounted Top mounted Top mounted 

60 m - vane ? 1.15 1.63 m 4.20 m 

45 m - cup ? 1.26 1.78 m 4.35 m 

43 m - vane ? 1.29 1.82 m 4.40 m 

30 m – cup ? 1.42 2.01 m 4.75 m 

28 m – vane ? 1.46 2.06 m 4.80 m 

15 m – cup ? 1.81 2.56 m 5.40 m 

Table 1.5 Recommended free sectors 

Level Sector Channel/signal 

62 0–360° CUP62M 

45 168–348° CUP45SV 

45 0–168° & 348–360° CUP45NO 

30 168–348° CUP30SV 

30 0–168° & 348–360° CUP30NO 

15 168–348° CUP15SV 

15 0–168° & 348–360° CUP15NO 

Figure 1.8 Boom orientation at the meteorological mast 






Figure 1.9 wake effects measured at 3 levels on the Horns Rev mast 

1.4.2 Primary met system 

Despite the poor accessibility to the measuring site, the practical problems encountered 

during the first three years of operation of the original meteorological systems have 

been few, and mainly restricted to damage due to lightning and mechanical damage 

caused by an extreme hurricane over Denmark on December 3, 1999. 

The top anemometer at level 62 m was struck by lightning in October 1999, and the 

sensor had to be replaced. Disassembly of the anemometer revealed severe damage to 

the rotor cup and to the bearing system caused by the induced overheating. The mast 

was equipped with lightning detectors, but unfortunately no lightning was detected 

during the measurement period. A technical investigation of the damaged anemometer 

demonstrated that the lightning induced current was beneath the detection range (~ 1000 

A) of the sensors, which explains why no lightning was recorded for October 1999. 

During the storm on December 3, 1999, parts of the electrical system were pushed out 

of their sockets as large waves impinged on the walls of the measurement shed located 

at level 6.2. This disconnected the power supply to the primary measuring system and 

hence caused a total system shut-down. Fortunately, the redundant measuring system 






continued to record data ensuring full data coverage from the top section of the mast 

during the following 10 days of “power out”. 

When evaluating the outcome of the analysis, the following facts should be kept in 

mind: 

• The wind speed data have not been corrected due to over-speeding caused by 

boom distortion. The rotors of the cup anemometers have been raised more than 

55 cm above the mounting booms and the expected over-speeding amounts to less 

than 1% according to [1]. 

• To reduce the considerable effect of flow distortion (mentioned in [2]) from the 

lattice mast, wind speed sensors placed at opposite sides of the mast are used 

when evaluating the statistical values for the lower levels of the mast (45, 30 and 

15 m). For these levels, wind speed data are selected from the up-wind side of the 

mast. 

It should be noted that the actual measuring levels are influenced by the changing sea 

levels due to the changing tides and sea swells at the Horns Rev site. In the analysis 

below there have been no attempts at neutralising the influence from the changing sea 

levels. The sea levels changes from 1.31 m below DNN (Danish Normal Zero) to 2.80 

m above DNN can be seen from Table 6.2. 

Figure 1.10 Example of data from wind speed sensor at level 62 m, primary met system 

10 min. mean values 

1.4.3 Back-up met system 

On the whole, the Back-up met system shows low data coverage; however, it should be 

noted that for a considerable period of time (April to September 2000) the sensor 

battery was low due to insufficient maintenance. 






Figure 1.11 Example of data from wind speed sensor at level 58 m, Back-up met system 

10-min. mean values 

1.4.4 Sonic system 

The sonic system shows very low data coverage because of problems with the sensors, 

data transmission from the sensor to the storage unit, low power capacity from the 

batteries, data storage on a lap top, and - of course - the access to the met mast. The 

maintenance visits to the met mast are very expensive, and therefore failures of the 

sonic system are not been repaired until next scheduled maintenance visit, or until 

several systems need maintenance. 

2. Statistics 

To give an overview of the wind records compiled from May 1999 to November 2002 

at Horns Rev, this section evaluates the main characteristics of the data. 

2.1 Wind speed and turbulence 

Main statistical values for the measuring period: 

Table 2.1. Main statistical 10-min mean values data, May 1999 to November 2002 

Height 62 45 30 15 

Mean Wind Speed [m/s] 

Max. Wind Speed [m/s] 

Mean Wind Direction [º] 

Mean Turbulence Intensity [-] 

Weibull Scale Parameter [m/s] 

Weibull Shape Parameter [-] 

Wind Shear (to nearest) 

9.46 

45.4 

254 

0.079 

10.59 

2.3 

0.16 

8.85 

43.1 

254 

0.09 

10.05 

2.3 

0.10 

8.51 

40.7 

254 

0.092 

9.64 

2.3 

0.10 

7.89 

39.5 

- 

0.107 

8.98 

2.2 

- 






The wind speed distribution at 62 m shown in Figure 2.1 is evaluated as the relative 

number of observations by 1 m/s wind speed bins for all direction sectors at 62 m 

height. 

Observations [%] 

Figure 2.1 Frequency distribution of wind speeds level 62 m from measurements, April 

1999 to November 2002 

Windspeed [m/s] 

10% 

9% 

8% 

7% 

6% 

5% 

4% 

3% 

2% 

1% 

0% 

14 

12 

10 

8 

6 

4 

2 

0 

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 

Wind Speed [m/s] 

1 2 3 4 5 6 7 8 9 10 11 12 

Month 

Figure 2.2 Monthly variation of average wind speed, May 1999 to November 2002 

W 

S 

E 

N 

Level62 

Level45 

Level30 

Level15 







Figure 2.3 Seasonal variation of wind speed day-to-day at level 62 m, May 1999 to 

November 2002 

Since the hour-by-hour variations in Figure 2.4 are based on data from 2000 and 2001 

only, no seasonal variations of the data coverage influence the result. 


14 

12 

10 

8 

6 

4 

2 

0 

10.2 

10 

9.8 

9.6 

9.4 

9.2 

9 

1 2 3 4 5 6 7 8 9 10 11 12 

Month 

8.8 

0 4 8 12 16 20 24 

Hour 

Level62 

Level45 

Level30 

Level15 

Figure 2.4 Diurnal variations of wind speed hour-by-hour at level 62 m, 2000 and 2001 

only 

2000 

2001 






Turbulence Intensity [%] 

20% 

18% 

16% 

14% 

12% 

10% 

8% 

6% 

4% 

2% 

0% 

0 2 4 6 8 10 12 14 16 18 20 22 24 26 


Figure 2.5 Variation of mean turbulence intensity with wind speed at level 62 m, May 


The mean turbulence intensity at level 62 m is 0.079. Figure 2.5 shows the distribution 

of turbulence intensity versus wind speed. The turbulence intensity is high at low wind 

speeds, decreases to a minimum between 8 and 12 m/s, and increases again with 

increasing wind speed, probably due to increasing wave height. 

270 

300 

240 

330 

210 

11% 

10% 

9% 

8% 

7% 

6% 

0 

180 

Figure 2.6 Mean turbulence intensity at each measurement level and each sector, May 


30 

150 

60 

120 

90 

kote15 

kote30 

kote45 

kote62 






PDF 

Figure 2.7 Frequency distribution of wind speed and the Weibull fit with different k 

parameters, May 1999 to November 2002. 

Exceedence probability 

10% 

9% 

8% 

7% 

6% 

5% 

4% 

3% 

2% 

1% 

0% 

100% 

90% 

80% 

70% 

60% 

50% 

40% 

30% 

20% 

10% 

0% 

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 

Wind speed level +62 (m/s) 

Measured 

Figure 2.8 Exceedence of probability of 10-min wind speed at level 62 m, May 1999 to 

November 2002 

k=2.2 

k=2.3 

k=2.4 

k=2.0 

0 5 10 15 20 25 

10 min. Wind speed, level +62 (m/s) 






2.2 Wind direction 

As expected, the winds are mainly south-westerly. The directional distribution is found 

as the relative number of observations by direction sectors of 30°. 

W 

14% 

12% 

10% 

8% 

6% 

4% 

2% 

0% 

N 

S 

Figure 2.9 Wind rose showing frequency directional distribution level 60 m. Distance 

from origin is the frequency of samples. May 1999 to November 2002 

E 






Figure 2.10 Mean wind speed distribution. Distance from origin is the mean wind speed 

in m/s. May 1999 to November 2002 

2.3 Ambient temperatures 

Frequency [pct] 

9 

8 

7 

6 

5 

4 

3 

2 

1 

0 

-10 

-8 

-6 

-4 

W 

-2 

0 

2 

4 

N 

12 

Figure 2.11 Temperature distribution at level 55 m for 2001 only 

6 

11 

10 

9 

8 

7 

6 

8 

S 

10 

12 

14 

Degree centigrade 

16 

18 

20 

E 

22 

24 

26 

28 

30 






Degrees centigrade 

Figure 2.12 Daily mean temperature at level 55 m, May 1999 to November2002 

Degrees centigrade 

18 

16 

14 

12 

10 

25 

20 

15 

10 

8 

6 

4 

2 

0 

5 

0 

0 25 50 75 100 125 150 175 200 225 250 275 300 325 350 

Day number 

1 2 3 4 5 6 7 8 9 10 11 12 

Month 

Figure 2.13 Monthly mean temperature at level 55 m, May 1999 to November2002 






Degree centigrade 

9.6 

9.5 

9.4 

9.3 

9.2 

9.1 

9 

8.9 

8.8 

0 4 8 12 16 20 24 

Hour 

Figure 2.14 Daily variation of mean temperature at level 55 m, 2000 and 2001 only 






2.4 Wind profiles 

Level above DNN [m] 

70 

60 

50 

40 

30 

20 

10 

0 

Measured 

Z0=0.0002 

Z0=0.002 

Z0=0.01 

0.0 2.0 4.0 6.0 8.0 10.0 


Figure 2.15 Average wind speed profile all sectors. Data from May 1999 to November 

2002. 

Wind speed profiles offshore are expected to conform to logarithmic profiles, but when 

looking at the observed average wind speeds at the four levels in Figure 2.16, the 

figures reveal that the wind speeds at 62 m are somewhat higher than could be expected 

from a logarithmic prediction. 






Level above DNN [m] 

(Lognormal scale) 

100 

10 

Figure 2.16 Semi-logarithmic plot of observed wind speeds by height. Wind speeds are 

averaged for all sectors. May 1999 to November 2002 

[8] discusses different factors that will lead to distortion of the profile away from 

logarithmic predictions, and it is worth noting that [8] has found the same tendency for 

other offshore sites in Denmark. At the moment, no further analyses have been initiated 

to clarify this subject here. 

3. 3-D measurements 

3.1 Sonic measurement system - basic statistics 

All the 3-D sonic time series are measured 50 m above sea level, and are stored in a 

common file format in the Database of Wind Characteristics 1 [3] where Table 3.1 

summarises the annual recordings. The data quality of the sonic measurements has been 

improved during the measurement period, and time series recorded after September 

2001 include a sonic temperature and a limited number of spikes (approx. 4000 hours). 

This section contains a number of plots based on statistical values extracted from [3]. 

1 Database on Wind Characteristics (http://www.winddata.com/) 

Measured 

7.0 7.5 8.0 8.5 9.0 9.5 10.0 







Table 3.1 Summary of sonic time series, measured at Horns Rev 

Year Hours Days Size 

1999 310 15 397 MB 

2000 773 36 991 MB 

2001 5634 242 5.62 GB 

2002 2184 93 1.25 GB 

Total 8902 386 8.26 GB 

The estimated Weibull distribution based on the sonic u–component measurements is 

(A=10.6 m/s, k=2.42, U= 9.36 m/s), and Figure 3.1 shows that the wind speed range 5– 

25 m/s is represented very well. The component turbulence intensity including standard 

deviation is shown as a function of sonic speed on Figure 3.1, and the average 

turbulence is listed in Table 3.2. The turbulence intensity increases as expected for an 

offshore site, due to increased wave height. 

Figure 3.1 3-D turbulence at Horns Rev, h=50 m asl 

Table 3.2 Average 3-D turbulence at Horns Rev, h=50m asl 

Turbulence V=10 m/s V=15 m/s V=20 m/s V=25 m/s 

TIu 6.3% 6.8% 8.2% 8.6% 

TIv 5.4% 5.5% 6.3% 7.0% 

TIw 3.4% 3.6% 4.2% 4.7% 






The average sonic tilt angle (deviation from horizontal plane) is shown on Figure 3.2 

together with the frictional velocity (u*) as a function of the sonic speed. The increase 

in the frictional velocity u* reflects the increased roughness length. 

Figure 3.2 Flow angle (tilt) and frictional velocity u* measured at Horns Rev, h=50 m 

The 3’ order (skewness) and 4’ order (kurtosis) moments for each sonic component are 

shown as a function of the sonic speed in Figure 3.3, Figure 3.4 and Figure 3.5. The 3’ 

moment and the matching standard deviation reflect the gustiness of the wind 2 , where 

negative skewness indicates negative gusts (lulls). 

Figure 3.3 3’ and 4’ order moments of the sonic u-component measured at Horns Rev, 

h=50 m asl 

2 The Gaussian distribution is characterized by skewness equal to 0 and kurtosis equal to 3. 






Figure 3.4 3’ and 4’ order moments of the sonic v-component measured at Horns Rev, 

h=50 m asl 

Figure 3.5 3’ and 4’ order moments of the sonic w-component measured at Horns Rev, 

h=50 m asl 

An example of measured 3-D time series including sonic temperature is shown in 

Figure 3.6. This time series contains a (large) gust of approx. 10 m/s and with a 

skewness of 2.8; a gust of this nature is however not severe to any wind turbines, 

because the gust rise time is rather long (>40 s). 






Figure 3.6 example of measured 3-D time series 

4. Updating resource estimates 

It is well-known that short-term measurements do not capture the full-range of 

variability of wind speeds at a site. The aim of this section is to use different methods to 

assess the wind resource at the offshore measurement site based on long-term 

(climatological) data sets. The purpose of using different methods is that each 

methodology has different strengths and weaknesses and by comparing the results the 

uncertainty of the analysis can be estimated. 

4.1 Characterising the long-term climate at Horns Rev 

Data from the offshore meteorological mast at Horns Rev are compared with those from 

the land-based meteorological station at Hvide Sande. Since data are available from 

Hvide Sande covering the period 1989 to 2002, the measurements at the site capture the 

long-term variability of wind speeds in western Denmark. By establishing a relationship 

between the data at the offshore site and the land-based Hvide Sande site for the period 






of simultaneous measurements (May 1999 to October 2002), data from the offshore site 

can be corrected to allow for the fact that the climate during the period of measurement 

may differ from the climate from a long-term perspective. 

An approximate value for the mean wind speed at Horns Rev can be obtained using a 

straightforward comparison of the two periods. The mean long-term wind speed at a 

height of 27.5 m at Hvide Sande is 7.14 m/s, but with 6.91 m/s 3.2% lower during the 

overlap period. It is therefore to be expected that the mean wind speeds at Horns Rev 

are approximately 3.2% higher than the 9.49 m/s measured during the overlap period, 

i.e. approx. 9.79 m/s. 

In the following sections, the methodologies used in the previous analysis are employed 

to update the wind resource estimates for Horns Rev. These results are then compared 

with those conducted in previous correlation analyses performed by Tech-wise and 

Risoe. 

It should be noted that mast shadow corrections have not been used to correct neither 

the Horns Rev data nor the long-term data set from Hvide Sande for the following 

reasons: 

1. To retain comparability with previous analyses. 

2. All wind resource estimates are performed based on the wind speeds from the 

top anemometer, which is expected to exhibit the least mast shadow effects in 

the record. 

3. Because it is not possible to correct data from Hvide Sande. 

4.2 Resource estimates using different methodologies 

Different methodologies are employed to reduce the uncertainties of the predicted wind 

speeds. However, the Weibull correction and measure-correlate-predict (MCP) methods 

do not account for the differences in directional distribution between predictor and 

predictand sites. 

4.2.1 Weibull method 

The Weibull correction method for extrapolating wind speed data series is based on the 

concept of modifying the Weibull parameters to characterise a longer data sampling 

period (as described in section 4.1). The method was developed and described in[4], but 

in brief is employed as follows: 






1. A data period is chosen where wind speeds from both 62 m Horns Rev and 27.5 

m at Hvide Sande mast are available. The 27.5 m level from Hvide Sande is 

chosen as a long time series representative of the ”average” wind climate. 

2. Weibull shape (A) and scale (k) factors are determined for each of the 12 wind 

sectors for both sites and the differences between the two sites are calculated as 

a correction factor for both A and k. 

3. The correction factors calculated for the shape and scale parameters between 

Horns Rev and Hvide Sande are applied to the Weibull factors calculated for the 

long data set at Hvide Sande. 

There are two variations of this method - direct correction of A and k parameters [4], or 

using the first and third moments to conserve the total energy of the sector-wise 

distributions [5]. The first method is used here. 

Table 4.1 Weibull shape and scale factors at Hvide Sande (27.5 m) and Horns Rev (62 

m), May 1999 to October 2002 

Hvide Sande Horns Rev 

Correction 

factors 

Sector A k % A k % A k 

mean 7.81 2.23 100.0 10.71 2.33 100.0 1.37 1.04 

N 5.46 1.95 4.3 8.65 2.11 5.1 1.59 1.08 

NNE 6.20 1.93 4.4 8.86 2.05 4.3 1.43 1.07 

ENE 6.63 2.40 4.4 8.15 2.35 4.4 1.23 0.98 

E 8.44 2.99 7.9 9.98 2.55 6.6 1.18 0.85 

ESE 8.48 2.72 9.4 11.35 2.81 8.9 1.34 1.03 

SSE 7.15 2.37 7.3 10.96 2.74 6.5 1.53 1.16 

S 7.56 2.42 7.9 11.28 2.63 8.7 1.49 1.08 

SSW 8.10 2.39 10.4 11.50 2.40 11.5 1.42 1.01 

WSW 8.08 2.23 11.5 11.08 2.23 12.1 1.37 1.00 

W 8.15 2.14 12.0 10.94 2.28 11.1 1.34 1.06 

WNW 8.61 2.07 13.5 11.27 2.29 11.4 1.31 1.11 

NNW 7.15 2.30 7.3 10.55 2.28 9.6 1.48 0.99 

Mean Wind Speed Hvide Sande 6.9 m/s 

Mean Wind Speed Horns Rev 9.5 m/s 






Table 4.2 Weibull shape and scale factors at Hvide Sande (27.5 m) and corrected 

Weibull parameters for Horns Rev (62 m), January 1989 to October 2002 

Hvide Sande Horns Rev 

Sector A k % A k % 

mean 8.06 2.24 100.0 11.05 2.34 100.0 

N 5.49 1.92 3.8 8.71 2.08 3.8 

NNE 6.54 2.08 4.3 9.36 2.22 4.3 

ENE 7.55 2.46 5.5 9.29 2.41 5.5 

E 8.68 2.79 8.3 10.27 2.37 8.3 

ESE 8.14 2.43 8.7 10.89 2.51 8.7 

SSE 6.84 2.38 6.7 10.49 2.75 6.7 

S 7.33 2.41 8.4 10.94 2.61 8.4 

SSW 7.91 2.50 10.5 11.23 2.51 10.5 

WSW 8.70 2.34 11.4 11.93 2.33 11.4 

W 8.89 2.20 12.2 11.94 2.35 12.2 

WNW 9.30 2.32 13.9 12.17 2.58 13.9 

NNW 6.99 2.03 6.1 10.31 2.01 6.1 

Mean Wind Speed Hvide Sande 7.1 m/s 

Mean Wind Speed Horns Rev 9.7 m/s 

4.2.2 Measure-correlate-predict (MCP) 

The MCP extrapolation methodology assumes a linear relationship between wind 

speeds at paired sites, where one site with long-term records acts as a predictor, and the 

wind speeds at a short-term measurement site are the predictand. Once a regression 

equation has been conditioned-based on the measurement overlap period, the regression 

equation parameters can be used to derive an extended data record for the site of interest 

(the predictand site). 

Here this method is employed using one regression equation for each wind direction 

sector. The methodology used is: 

1. Produce a data set containing wind speeds and directions from Hvide Sande at 

27.5 m and from Horns Rev at 62 m with complete data overlap (that is no 

missing observations at either site). Assess whether the correlation between the 

wind speeds at the two sites is adequate to characterise the relationship Figure 

4.1. In this analysis all correlation coefficients were in excess of 0.79 Table 4.3. 

2. Use the data to generate a linear regression equation (based on least squares 

estimates) for each sector where: 

UHorns Rev = AHvide Sande + B 






A and B are constants. A describes the slope of the regression line and B is the 

intercept. 

3. Use the constants A and B in the above equation with data measured at Hvide 

Sande over the period January 1989 to October 2002 to generate a longer 

interpolated data series for Horns Rev. This can be used to calculate an average 

wind speed and as input to the WAsP model to generate energy density, 

potential power production for a given wind turbine, and Weibull shape and 

scale parameters. It should be noted that the directions used in the time series are 

those from Hvide Sande. Directions from Hvide Sande and Horns Rev during 

the overlap period are compared and shown in Figure 4.2 

The regression line can either be fitted through the origin or with an intercept depending 

on which gives the best fit to the data. A summary for all data using both methods is 

given below. 

Fit 1: Linear 

Equation Y = 1.1277 * X + 1.6885 

Number of data points used = 29606 

Average X = 6.889 

Average Y = 9.458 

Coefficient of determination, R-squared = 0.7111 

Fit 2: Through origin 

Equation Y = 1.328 * X 

Number of data points used = 29606 

Average X = 6.889 

Average Y = 9.458 

Coefficient of determination, R-squared = 0.6836 

Since linear fit gives the highest r 2 , this fit has been used in the following analysis, and 

is the line shown in Figure 4.1. 






Wind speeds at Horns Rev (m/s) 

40.00 

30.00 

20.00 

10.00 

0.00 

y = 1.1277x + 1.6885 

R 2 = 0.7111 

0.0 10.0 20.0 30.0 40.0 

Wind speeds at Hvide Sande (m/s) 

Figure 4.1 Wind speeds at Horns Rev (62 m) and Hvide Sande (27.5 m), May 1999 to 

October 2002 






Wind direction at Horns Rev 

300 

200 

100 

0 

0 100 200 300 

Wind direction atHvide Sande 

y = 0.9555x 

R 2 = 0.4131 

Figure 4.2 Wind direction at Horns Rev and Hvide Sande, May 1999 to October 2002. 

The line is a linear fit through the origin where Dir Horns Rev = Dir Hvide Sande * 

0.956. The correlations coefficient is 0.64 

Table 4.3 MCP analysis, May 1999 to October 2002. A is the slope of the regression 

line, and B the offset of the regression line 

Sector AvgHS AvgHR AvgHR/HS RegCoeff A Offset B Corr.Coef. 

m/s m/s -- m/s m/s -- 

N 4.33 7.45 1.722 1.282 1.901 0.799 

NNE 5.44 7.93 1.459 1.125 1.817 0.815 

ENE 5.86 7.63 1.304 0.871 2.532 0.820 

E 7.70 9.96 1.293 1.060 1.796 0.823 

ESE 7.86 10.34 1.315 1.089 1.780 0.855 

SSE 6.37 10.17 1.596 1.435 1.030 0.830 

S 6.84 10.67 1.560 1.353 1.420 0.894 

SSW 7.26 10.80 1.487 1.335 1.108 0.911 

WSW 7.32 9.67 1.322 1.227 0.699 0.899 

W 7.60 9.09 1.196 1.175 0.160 0.894 

WNW 8.26 9.85 1.194 1.126 0.561 0.895 

NNW 5.71 8.90 1.558 1.265 1.670 0.834 

These regression coefficients are applied to the long time series at Hvide Sande to give 

an estimate of the long-term mean wind parameters at Horns Rev. This gives a mean 






wind speed of 9.67 m/s, Weibull A parameters of 10.8 m/s and Weibull k parameter of 

2.5. 

4.3 Comparison with previous estimates 

Table 4.4 shows a comparison of wind speeds and Weibull factors generated for this 

analysis, and a comparison with previous estimates from [4], [5] and [6]. 

The results contained in this report are in good agreement with those obtained 

previously, although it should be noted that the measured values are lower than the 

long-term mean. Please note that nearly 30,000 records were used in the analysis – onsite 

measurements were not used in [4] and [5]. 

Table 4.4 Comparison of wind resource estimates of wind speeds at Horns Rev 

Method Data Source U 48 m A k 

Energy density 

48m 

(m/s) (m/s) (W/m^2) 

Horns Rev 

Best estimate Lightship (Højstrup et al., 1997) 9.1 10.2 2.2 800 


WAsP Lightship (Barthelmie et al., 1998) 9.2 10.4 2.2 844 

WAsP Tjæreborg (Barthelmie et al., 1998) 9.72 11 2.4 933 


Best estimate Lightship (Barthelmie et al., 1998) 9.2 10.4 2.3 810 

Method Data Source U 62 m A k 

MCP 

MCP 

MCP 

Weibull 

Horns Rev 99-01 

/ Juvre met mast Tech-wise report no. 01-079 2001 


/ Tjæreborg met 

9.94 

mast Tech-wise report no. 01-079 2001 10.1 


/ Hvide Sande Tech-wise report no. 01-078 2001 9.72 

Energy density 

48m 

(m/s) (m/s) (W/m^2) 


/ Hvide Sande This report 9.79 11.05 2.34 898 


MCP / Hvide Sande This report 9.67 10.8 2.5 801 

Observed Horns Rev 99-02 This report 9.49 10.71 2.33 820 

Best estimate 


/ Hvide Sande This report 9.79 






5. Stability and climate 

The atmospheric stability is a derived quantity, which is based on the Richardson 

number, as defined by the formula: 

The temperature difference is based on temperature recordings from level 13 and 55 m, 

while the wind speed difference is based on wind speeds from level 15 and 45 m: 

Table 5.1 Stability distribution for 5 = CUP62M < 25 m/s 

Stability Interval Distribution 

Very stable 0.12 = Ri < 1 37% 

Stable 0.045 = Ri < 0.12 11% 

Near neutral -0.06 = Ri < 0.045 9% 

Unstable -0.30 = Ri < -0.06 12% 

Very unstable -2.00 = Ri < -0.30 31% 

The stability analysis is based on 11,550 hours of measurements recorded in the wind 

speed interval 5–25 m/s, and Figure 5.1 shows the stability distribution representing the 

Horns Rev site, according to the definition given in Table 5.1. 

pdf [%] 

40 

30 

20 

10 

Ri 

5.1 Shear exponent distribution 

0 

Very stable 

g Δt 

Δh 

= × 

T ( ΔV 

Δh 

2 

) 

Stability measured at Horns Rev 

5 < CUP62M < 25 m/s 

Slightly stable 

Near neutral 

Slightly unstable 

Figure 5.1 Stability distribution 

Very unstable 

The shear exponent a is a derived quantity, which is used to represent the mean wind 

gradient: 






V h 

= V 

10 

⎡ h ⎤ 

× 

⎢ ⎥ 

⎣10 

⎦ 

The shear exponent is fitted for each 10-min period, based on free, undistrubed wind 

speed signals at levels 15, 30, 45 and 62 m. The average shear exponents, with reference 

to the wind speed at level 62 m, are listed in Table 5.2 for each wind speed bin. 

Table 5.2 Bin average wind shear exponent. 

Interval Hours < a > 

4 < V62 ≤ 6 m/s 3140 0.10 

6 < V62 ≤ 8 m/s 4018 0.12 

8 < V62 ≤ 10 m/s 4400 0.13 

10 < V62 ≤ 12 m/s 3950 0.12 

12 < V62 ≤ 14 m/s 2963 0.12 

14 < V62 ≤ 16 m/s 1994 0.12 

16 < V62 ≤ 18 m/s 1222 0.11 

18 < V62 ≤ 20 m/s 589 0.12 

V62 > 20 m/s 413 0.12 

The wind shear exponent distribution for two wind speed intervals has been determined 

and Figure 5.2 shows the distributions. 

Figure 5.2 Distribution of shear exponent at Horns Rev 

5.2 Distribution of gusts 

The maximum 10-min speed values lasting 1 and 5 s have been recorded. The analysed 

data represents 23,538 hours of measurements for wind speeds higher than 4.5 m/s. The 

gust size presented in this section is the difference between the short-term maximum 

value and the 10-min mean wind speed. 

α 






The bin averaged gust size, as a function of wind speed is shown on Figure 5.3 a, where 

only a small amount of data is recorded at wind speeds above 35 m/s (during the 

December storm in 1999). 

The distributions of 5-s gusts at level 62 m have been determined for 4 different wind 

speed intervals (V > 10 m/s) based on the figures given in Table 5.3. 

Table 5.3 Number of hours in each wind speed interval 

Interval Hours 

10 < V < 15 m/s 8506 hours 

15 < V < 20 m/s 2791 hours 

20 < V < 25 m/s 365 hours 

25 < V 47 hours 

Figure 5.3 Distributions of gusts with a reference period of 5 s, for each wind speed 

interval 






6. Wind-wave-roughness 

Wave measurements have been made simultaneously with meteorological 

measurements at the Horns Rev site. Site and wind data are described in section 1. 

Simultaneous wind and wave data are available from June 1999 to November 2002. 

The wave-measuring instrument is a Waverider. The Waverider is a buoy which, 

following the movements of the water surface, measures waves by measuring the 

vertical acceleration of the buoy. The discrepancy between the vertical movements of 

the Waverider and the movements of the sea surface is small. When a moored 

Waverider follows the waves, the force of the mooring line will change. This force is 

produced by the changing immersion of the buoy, resulting in an error of max 1.5%. 

The measurements are transferred onshore via a HF radio link, stored in the database, 

and displayed on the web page http;//212.130.241.250/hornsrev/ within less than one 

hour. In the first phase of the measuring period, there were two Waveriders operating 

simultaneously, see 

Figure 6.1 






Figure 6.1 Location of marine measurements of wave (Waverider) and current 

(Workhorse) at Horns Rev 






Figure 6.2 Waverider used for wave height measurements 

The current-measuring instrument is a Workhorse Sentinel ADCP. The Workhorse is an 

Acoustic Doppler Current Profiler that when placed on the seabed sends acoustic 

signals up towards the surface. Acoustic reflections from the water particles are 

transformed to current measurements. 

Figure 6.3 Workhorse Sentinel ADCP used for current measurements 

6.1 Marine data overview 

Table 6.1 Data coverage for the marine measurements systems 

Measuring System Data Period Hours Data Coverage 

Waverider South 1999.07.01 2002.12.12 30242 80.52% 

Waverider North 1999.07.01 2000.08.31 10246 91.01% 

Workhorse ADCP 1999.07.01 2002.10.25 29087 64.34% 






6.2 Marine statistics 

Table 6.2 gives an overview of the most important parameters measured stating the 

mean and maximum values. The WL is referred to the DNN (Danish Normal Zero) 

system. 

Table 6.2 Mean and max. values of the most interesting marine parameters recorded 

Waverider South 

(note that Hmax has only been 

measured since Nov. 1, 1999) 

Waverider North 

(note that Hmax has only been 

measured since Nov. 1, 1999) 

Current 

(middle of water column) 

Water Level 

(rel. to DNN) 

6.2.1 Time series plots 

Unit Mean Max. 

Hs 1.09 m 4.32 m 

Hmax 1.65m 7.64 m 

T02 4.11 s 8.30 s 

Tp 6.22 s 25.0 s 

Hs 1.29 m 4.48 m 

Hmax 2.55 m 7.40 m 

T02 4.32 s 8.17 s 

Tp 6.74 s 16.7 s 

Abs. current 0.35 m/s 0.91 m/s 

North Component -0.85 m/s / 0.83 m/s 

East Component -0.42 m/s / 0.75 m/s 

0.49 m -1.31 m / 2.80 m 

Two examples of time series of wind speeds at a height of 15 m, wind directions and 

significant wave heights are shown in Figure 6.4 and Figure 6.5. The plots show 

relatively good agreement between wave height and wind speed. 






Wind direction 

Wind Speed 15m 

350 

300 

250 

200 

150 

100 

50 

0 

14.0 

12.0 

10.0 

8.0 

6.0 

4.0 

2.0 

0.0 

2002-08-31 12:00 

2002-09-01 00:00 

2002-09-01 12:00 

2002-09-02 00:00 

2002-09-02 12:00 

2002-09-03 00:00 

2002-09-03 12:00 

2002-09-04 00:00 


Wave Height Hs 

2002-09-04 12:00 

2002-09-05 00:00 

2002-09-05 12:00 

Figure 6.4 Example of a time series of wind speeds at 15 m, wind directions and 

significant wave heights at Horns Rev, September 1–5, 2002 




in energy and environment DK-7000 Fredericia 

2.5 

2.0 

1.5 

1.0 

0.5 

0.0 

Wave Height Hs


Wind direction 


350 

300 

250 

200 

150 

100 

50 

0 

18.0 

16.0 

14.0 

12.0 

10.0 

8.0 

6.0 

4.0 

2.0 

0.0 

2001-08-26 12:00 

Figure 6.5 Example of a time series of wind speeds at 15 m, wind directions and 

significant wave heights at Horns Rev, August 27–31, 2001 

6.2.2 Waves 

2001-08-27 00:00 

2001-08-27 12:00 

2001-08-28 00:00 

2001-08-28 12:00 

2001-08-29 00:00 

2001-08-29 12:00 

2001-08-30 00:00 


Wave Height Hs 

2001-08-30 12:00 

2001-08-31 00:00 

2001-08-31 12:00 

The distribution of the significant wave height is shown in Figure 6.6, the same figure 

also shows the Log Normal distribution with parameters a1 = 0.35 and a2 = 0.55. The 

distribution is based on more than 14,000 hours of data recorded from July 1999 to 

November 2002. 





2.5 

2.0 

1.5 

1.0 

0.5 

0.0 

Wave Height Hs


pdf[%] 

7 

6 

5 

4 

3 

2 

1 

0 

Measure 

LogNormal 

0 1 2 3 4 5 6 7 

Significant Wave Hight [m] 

Figure 6.6 Probability distributions of significant wave height Hs 

The distribution of the mean wave height is shown in Figure 6.7 the same figure also 

shows the Log Normal distribution with parameters a1 = -0.15 and a2 = 0.60. 






pdf [%] 

10 

9 

8 

7 

6 

5 

4 

3 

2 

1 

0 

Measure 

LogNormal 

0 1 2 3 4 5 

Mean Wave Hight 

Figure 6.7 Probability distributions of mean wave height Hmean 

Since waves are generated by the wind shear and wind pressure on the sea surface, a 

clear dependency on these two phenomena can be expected. Figure 6.9 illustrates this 

relationship between the wind speed (1 hour average) in level 62 and the significant 

wave height Hm0. In addition to the wind speed it is evident from this figure that also the 

fetch plays an important role for the wave generation, waves being smaller from eastern 

directions where the fetch is limited (15–40 km). The pronounced scatter in the figure 

can mainly be contributed to the fact that the waves do not react instantaneously to fast 

changes in wind speed. 






Significant wave height [m] 

4 

3.5 

3 

2.5 

2 

1.5 

1 

0.5 

0 

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 

Wind speed at kote 15 [m/s] 

Figure 6.8 Significant mean wave height versus wind speed bin at level 15 m 

Dependencies between different parameters are less distorted by deviations between 

measurement period and long-term average than probability distributions. Therefore, 

scatter plots are useful to validate model results for the measured parameters. Plots 

showing the dependency of wave on parameters on wind speed and direction are given 

in Figure 6.9 and for each sector in Figure 6.10 and Figure 6.11. 






Wave height Hm0 [m] 

5 

4 

3 

2 

1 

0 

0 10 20 30 40 50 

Wind speed [m/s] 

Figure 6.9 Measured relationships at Horns Rev (Waverider south) between wind 

speeds (level 62) and significant wave heights for 12 directions. May 1999 

to November 2002 

For wind speeds up to about 20 m/s, there is an almost linear relationship between wind 

speed and wave height. For higher winds, the waves seem to reach an upper limit of 

about 4 m. This limit is governed by the water depth which, when sufficiently shallow, 

forces the waves to break. Hence the extreme wave conditions are not limited by the 

wind, but rather by the water level. 

The relationship between the significant wave height Hm0 and the maximum wave 

height Hmax is illustrated in Figure 6.12 by the ratio Hmax/Hm0. Despite the inherent 

scatter, a weak trend towards a falling Hmax/Hm0-ratio can be observed for higher waves. 

This can again be explained by breaking of the largest waves. 





N 

NNE 

ENE 

E 

ESE 

SSE 

S 

SSW 

WSW 

W 

WNW 

NNW


Hm0 (m) 

Hm0 (m) 

Hm0 (m) 

Wind direction N y = 0.1108x 

5.0 

4.5 

4.0 

3.5 

3.0 

2.5 

2.0 

1.5 

1.0 

0.5 

0.0 

0 10 20 30 

WS62 (m/s) 

Wind direction ENE 

y = 0.0917x 

5.0 

4.5 

4.0 

3.5 

3.0 

2.5 

2.0 

1.5 

1.0 

0.5 

0.0 

0 10 20 30 

WS62 (m/s) 

Wind direction ESE 

y = 0.0795x 

5.0 

4.5 

4.0 

3.5 

3.0 

2.5 

2.0 

1.5 

1.0 

0.5 

0.0 

0 10 20 30 

WS62 (m/s) 

Hm0 (m) 

Hm0 (m) 

Hm0 (m) 

Wind direction NNE y = 0.1059x 

5.0 

4.5 

4.0 

3.5 

3.0 

2.5 

2.0 

1.5 

1.0 

0.5 

0.0 

0 10 20 30 

WS62 (m/s) 

Wind direction E 

y = 0.0781x 

5.0 

4.5 

4.0 

3.5 

3.0 

2.5 

2.0 

1.5 

1.0 

0.5 

0.0 

0 10 20 30 

WS62 (m/s) 

Wind direction SSE 

y = 0.0987x 

5.0 

4.5 

4.0 

3.5 

3.0 

2.5 

2.0 

1.5 

1.0 

0.5 

0.0 

0 10 20 30 

WS62 (m/s) 

Figure 6.10 Wind speed at 62 m height versus significant wave heights for each sector 

of wind direction 






Hm0 (m) 

Hm0 (m) 

Hm0 (m) 

Wind direction S 

y = 0.1133x 

5.0 

4.5 

4.0 

3.5 

3.0 

2.5 

2.0 

1.5 

1.0 

0.5 

0.0 

0 10 20 30 

WS62 (m/s) 

Wind direction WSW 

5.0 

4.5 

4.0 

3.5 

3.0 

2.5 

2.0 

1.5 

1.0 

0.5 

0.0 

y = 0.1326x 

0 10 20 30 

WS62 (m/s) 

Wind direction WNW 

y = 0.1321x 

5.0 

4.5 

4.0 

3.5 

3.0 

2.5 

2.0 

1.5 

1.0 

0.5 

0.0 

0 10 20 30 

WS62 (m/s) 

Hm0 (m) 

Hm0 (m) 

Hm0 (m) 

Wind direction SSW 

y = 0.1211x 

5.0 

4.5 

4.0 

3.5 

3.0 

2.5 

2.0 

1.5 

1.0 

0.5 

0.0 

0 10 20 30 

WS62 (m/s) 

Wind direction W 

5.0 

4.5 

4.0 

3.5 

3.0 

2.5 

2.0 

1.5 

1.0 

0.5 

0.0 

y = 0.1338x 

0 10 20 30 

WS62 (m/s) 

Wind direction NNW y = 0.1207x 

5.0 

4.5 

4.0 

3.5 

3.0 

2.5 

2.0 

1.5 

1.0 

0.5 

0.0 

0 10 20 30 

WS62 (m/s) 

Figure 6.11 Wind speed at 62 m height versus significant wave heights for each sector 

of wind direction 






Hmax/Hmo 

3 

2.5 

2 

1.5 

1 

0.5 

0 

0 1 2 3 4 5 

Hmo (m) 

Figure 6.12 Ratio between Hmax and Hm0 (Waverider south data), May 1999 to 

November 2002 

Figure 6.13 shows the relationship between wave height (Hm0) and wave period (T02). 

The measured values can roughly be regarded as grouped in two clusters; an upper 

cluster where waves are generated by the wind and a lower cluster (Hm0 ≈ 0.5 m) where 

the waves originate from swells. 

The wind generated part of the waves shows that there is a well-defined relationship 

between wave height and wave period. 






Wave height Hm0 [m] 

5 

4 

3 

2 

1 

0 

0 2 4 6 8 10 

Wave period T02 [s] 

Figure 6.13 Relationship between Hm0 and T02 (Waverider south), May 1999 to 

November 2002 

Finally, the exceedence of probabilities of the significant wave heights measured at pos. 

south is plotted in Figure 6.14. 






Exceedance Probability 

100% 

90% 

80% 

70% 

60% 

50% 

40% 

30% 

20% 

10% 

0% 

Figure 6.14 Probability of exceedence for measured significant wave heights at 

positions south, May 1999 to November 2002 

A key point in selecting the right operation and maintenance (O&M) strategy for an 

offshore wind farm, is the accessibility of the wind turbines. The most natural choice of 

transport for offshore operations is by boat. However, with a limiting wave height of 

Hs=1.2-1.3 m for boat operations, it can be seen from Figure 6.17 that the accessibility 

is only approx. 60%. 

6.2.3 Currents 

0.0 0.5 1.0 1.5 2.0 2.5 3.0 

Significant wave height [m] 

The Horns Rev site is dominated by a N-S flowing tidal current with maximum 

velocities of about 1 m/s. In extreme storm conditions with winds from the west, the 

wind induced current in the eastward direction has been measured to nearly 0.8 m/s (the 

December 3, 1999 hurricane). 






Figure 6.15 Measured current magnitudes [m/s] and flow directions [°], July 1999 to 

December 2000 

Current profiles are shown in Figure 6.16. The blue line (WL) is the mean water level 

for the sample period of 15 min. waves on the surface results in the variation of the 

profile above the read line (maxbin). The workhorse can only make valid measurements 

approximately 1.5 m above its position at the seabed. Valid measurements are shown in 

Figure 6.16 from the red line to level -5.5 m. 

21.07.99 20:16 

N 

E 

WL 

Maxbin 

2 

1 

0 

-1 

-2 

-3 

-4 

-5 

-6 

-7 

-600 -300 0 300 600 

21.07.99 17:16 

N 

E 

WL 

Maxbin 

2 

1 

0 

-1 

-2 

-3 

-4 

-5 

-6 

-7 

-600 -300 0 300 600 

Figure 6.16 Plot of current profiles on July 21, 1999. X-axis Current [mm/s] Y-axis 

level [m] 

0 

0.2 

0.4 

0.6 

0.8 

1 






6.3 Numerical simulations models 

Prior to commencing the marine measurement programme, a numerical study was 

performed. The aim of this study was primarily to establish estimates of the long-term 

extremes of waves, currents, and water level. However, an important part of the study 

was also to estimate the accessibility of the turbines for different limiting sea conditions 

(values of Hs) and ”wave window lengths” [11]. 

The input for this study was a 15-year continuous meteorological data series covering 

the North Sea. These meteorological data were used as input to the MIKE OSW model 

(Danish Hydraulic Institute’s offshore wave model) to simulate a 15-year consecutive 

wave train in the proximity of the wind farm. Since the water depth is rather limited in 

and around the wind farm, the OSW waves were used as input to a shallow-water wave 

model, which could then simulate the waves inside the wind farm site. 

Table 6.3 lists the extreme value analysis results for 10-, 50- and 100-year return 

periods. 

Table 6.3 Extreme values from numerical study [11] 

Parameter 10-year return period 50-year return period 100-year return period 

Hs 5.0 m 5.3 m 5.4 m 

Hmax 8.1 m 8.1 m 8.1 m 

Currents 0.79 m/s 0.88 m/s 0.92 m/s 

Water level -1.7 m / +3.0 m -2.4 m / +3.5 m -2.7 m / +3.7 m 

Comparing Table 6.3 with the measured values (Table 6.2) over the 3-year measuring 

period, the only divergence observed is that the measured currents exceed the long-term 

predictions. However, this is fully expected as the current meter is located close to the 

met mast on a water depth somewhat lower than the average water depth in the wind 

farm site, which was used in the numerical simulations. 

The analysis of ”wave windows” was made on a monthly basis. In Figure 6.17 the 

accessibility, assuming that Hs permanently has to be below 1.3 m in time periods of 12, 

24 and 72 hours, is plotted for each month. The accessibility in the winter season can be 

as low as 20% whereas the summer offers an accessibility of 70–80%. 






100% 

90% 

80% 

70% 

60% 

50% 

40% 

30% 

20% 

10% 

0% 

Accessibility for H s


Turbulence intensity at kote 15 


0.13 

0.12 

0.11 

0.1 

0.09 

0.08 

0.13 

0.12 

0.11 

0.1 

0.09 

0.08 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 

Sig. wave height [m] 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 


Figure 6.18 Bin averaged turbulence intensity at 15 m versus significant wave height 

for different wind speed classes 


0-2m/s 

2-4m/s 

6-8m/s 

8-10m/s 

10-12m/s 

12-14m/s 







0.13 

0.12 

0.11 

0.1 

0.09 

0.08 

0.13 

0.12 

0.11 

0.1 

0.09 

0.08 

0 0.5 1 1.5 2 2.5 3 3.5 4 

Figure 6.19 Bin averaged turbulence intensity at 15 m versus significant wave height 

for different wind speed classes 

7. Extreme events 


0 0.5 1 1.5 2 2.5 3 3.5 4 


On December 3, 1999 Denmark was hit by a hurricane exhibiting extremely fierce gusts 

- measurements from several places recorded speeds as high as 40-50 m/s. With wind 

speeds recorded of this magnitude, the hurricane was the fiercest in Denmark for more 

than 100 years. 

The Horns Rev site was hit by the hurricane in the afternoon with wind speeds (10-min. 

avg.) increasing from 15 m/s at noon to more than 45 m/s at 18.00 hours. The measured 


14-16m/s 

16-18m/s 

18-20m/s 

20-22m/s 

22-24m/s 

24-26m/s 





maximum 1 Hz value of 58.5 m/s and a maximum 5-s running mean value of 53.4 m/s 

indicate very high gust values. 


70 

60 

50 

40 

30 

20 

10 

0 

10 min average 

5 sec average 

max wind speed 

Air press. 

00:00 06:00 12:00 18:00 00:00 

Time 

1010 

1000 

Figure 7.1 Measured wind speed level at 62 m and air pressure during the passage of 

the hurricane, December 3, 1999 - primary met system 

Figure 7.1 shows the wind speeds and air pressure at the culmination of the hurricane. 

The zenith of the hurricane lasted for about 2.5 hours, with two peaks divided by a 

distinct drop in wind speed in between. 

During the storm, parts of the electrical system were pushed out of their sockets - as 

earlier mentioned - as large waves, approximately 6 m plus 2 meter high water level, 

impinged on the walls of the measurement shed located at level 6.2 at about 23.50 

hours. This caused disconnection of the power supply to the primary measuring system, 

and hence a total system shut-down of the primary met system for the following 10 

days. 

990 

980 

970 

960 

950 

940 


Air Pressure [hpa] 





H (m) 

7.0 

6.0 

5.0 

4.0 

3.0 

2.0 

1.0 

0.0 

03-12 03-12 03-12 03-12 03-12 03-12 03-12 03-12 03-12 03-12 03-12 03-12 04-12 04-12 04-12 04-12 04-12 04-12 04-12 04-12 04-12 04-12 04-12 04-12 05-12 

00:00 02:00 04:00 06:00 08:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 00:00 02:00 04:00 06:00 08:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 00:00 

Time (UCT, add 1 hour to get Danish Winter Time) 

Figure 7.2 Waves and water level during the hurricane December 3–4, 1999 

Water level above DNN (cm) 

300.0 

250.0 

200.0 

150.0 

100.0 

50.0 

Water level 

Curr. Level +0.67 

Curr. Level -0.87 

Curr. Level -2.87 

Figure 7.3 Water level and current during the hurricane December 3–4, 1999 

Hs_north 

Hs_south 

Hmax_north 

Hmax_south 

Water level 

0.0 

0.00 

03-12 03-12 03-12 03-12 03-12 03-12 03-12 03-12 03-12 03-12 03-12 03-12 04-12 04-12 04-12 04-12 04-12 04-12 04-12 04-12 04-12 04-12 04-12 04-12 05-12 

00:00 02:00 04:00 06:00 08:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 00:00 02:00 04:00 06:00 08:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 00:00 

Time (UCT, add 1 hour to get Danish Winter Time) 





300 

250 

200 

150 

100 

50 

0 

-50 

1.00 

0.90 

0.80 

0.70 

0.60 

0.50 

0.40 

0.30 

0.20 

0.10 

WL (cm) 

Current speed (m/s)


8. Uncertainties 

Offshore wind resources can be estimated without using on-site data, but are in that case 

subject to considerable uncertainty. Use of on-site data is always preferable, but using 

short time series is also a source of uncertainty since wind speeds also vary on a number 

of time scales from seconds to decades. Here an attempt has been made to reduce the 

uncertainties in the wind resource prediction at the offshore site by using a number of 

different methods to establish the relationship between the measured time series 

offshore and a reliable long-term time series at Hvide Sande. It is difficult to determine 

the relationship between onshore and offshore wind speeds, especially when only short 

time series are available. 

The Weibull correction method relies on correct fits of the Weibull distribution to the 

observed wind speed data in each sector. The MCP method typically predicts lower 

wind speeds than the other method: this is most likely due to the problem of correlating 

actual wind speed values. As the distance between the measurement and prediction site 

increases, the probability of introducing errors into the correlation also increases. 

The wave and current data shown in this report are direct plot of the measured data, no 

calculations and comparisons have been made, so uncertainties only depends on the 

uncertainty from the actual measuring instruments the Waverider and the Workhorse. 






9. Conclusion 

With meteorological data and marine data recorded for a period of 3.5 years, the 

meteorological aspects as well as the marine aspects of the Horns Rev site, are very well 

documented. In addition, the data coverage of the meteorological measurements is more 

than 99%; using the back-up system it would be possible to establish a data set with 

100% coverage. The report describes the three individual meteorological systems - 

main, back-up and sonic system - in detail. The measuring programme investigated the 

directional sensitivity for wake effects, as well as the affect of speed-up and wake effect 

on mast effects. 

The report evaluates the main statistical values to give an overview of the wind records 

compiled from May 1999 to November 2002. The statistics include the distribution of 

wind speed, wind direction and turbulence. 

More than 8900 hours of 20 Hz 3D-sonic measurements are available for the site. The 

sonic data are stored in a common file format in the Database on Wind Characteristics. 

The sonic data shown and evaluated in this report are based on statistical figures. 

Different methods have been applied to produce long-term predictions of the wind 

resources. The purpose of using different methods is that each methodology has 

different strengths and weaknesses. The wind resources estimated in this report are 

compared with previous estimates, and good agreement is seen. The report also 

evaluates the atmospheric stability, the shear exponent distribution and the distribution 

of gusts. 

Wave action has been measured simultaneously with the meteorological aspects of the 

site; the coverage exceeds 80% for wave height data and 60% for current data. The 

report presents statistical values and distribution plots. For further analysis, numerical 

simulations have been performed to establish estimates of the long-term extremes of 

waves, current and water level. 

During the measuring period, the site encountered an extreme hurricane, which is also 

described. The hurricane hit the Horns Rev site on December 3, 1999 and exhibited 

extremely fierce gusts with maximum 1 Hz values of 58.5 m/s at 18.00 hours. 

Finally, the report discusses uncertainties related to both meteorological and marine data 

as well as data treatment. 






10. References 

[1] IEC 61400-1: Wind turbine generator system - Part 1, Safety requirements. 

[2] Statistics of offshore wind speed gusts, EWEC2001, Copenhagen 2001 

[3] Database on Wind Characteristics, Internet database containing wind field 

measurements, URL=http://www.winddata.com/ 

[4] Offshore Wind Resources at Selected Danish Sites, J. Højstrup, B. Lange, R. J. 

Barthelmie, A. M. J. Pedersen, F. A. Olsen, J. Svenson. Risø June 1997. 

[5] Offshore Wind Resources at Danish Measurement Sites, R. J. Barthelmie, M. S. 

Courtney, B. Lange, M. Nielsen, A. M. Sempreviva, J. Svenson, F. Olsen, T. 

Christensen. Risø November 1998. 

[6] Produktionsestimat baseret på korrelation til Hvide Sande masten (in Danish: 

Production estimate based on correlation to the Hvide Sande mast), report 

no. 01-078 Søren Mogensen. Tech-wise 2001. 

[7] Korrelationsanalyse mellem Juvre og Horns Rev (in Danish: Correlation analysis 

between Juvre and Horns Rev), report no. 01-079 Søren Mogensen. Techwise 

2001. 

[8] R.J. Barthelmie, M.S. Courtney, B. Lange, M. Nielsen, A.M. Sempreviva. J. Svenson. 

F. Olsen, T. Christensen, 1999: Offshore Wind Resources at Danish 

Measurement Sites. European Wind Conference, 1- 5 March 1999, Nice, 

France, pp. 1101-1104. 

[9] Pedersen, B.M., K.S. Hansen, S. Øye, M. Brinch, O. Fabian, 1992: Some 

experimental investigations of the influence of the mounting arrangements 

on the accuracy of cup-anemometer measurements. Journ. Of Wind. Eng. 

and Ind. Aerod., vol 39, pp. 373-383. 

[10] J. Højstrup, 1999: Vertical Extrapolation of Offshore Wind Profiles. European 

Wind Conference, 1- 5 March 1999, Nice, France, pp. 1220-1223. 

[11] Dansk Hydraulisk Institut November 1999: Havvindmøllefundamenter ved Horns 

Rev. Hydrografiske Data (in Danish: Offshore wind farm foundations at 

Horns Rev. Hydrographic data).

Wind resources at Horns Rev

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